The first integral in the form given above is divergent with respect to the spatial frequency practical implementation of the formula replaces , where W is a window function that vanishes outside the interval The cut-off frequency can be shown to be inversely related to the ray-spacing for a consistent numerical calculation of the integral. When the filter is purely of the band-pass type , the Radon formula can be cast as a convolution integral:

(19)

where

and

The inner integral over s is one dimensional convolution and the outer integral, an averaging operation over is called back projection.This implementation of the convolution backprojection algorithm is commonly used in medical imaging. Applications of the CBP algorithm to flow and heat transfer problems have been reviewed by Munshi [94].

Figure 4.63: Nomenclature for the concolution backprojection algorithm